Suppose that you are an accident investigator and you are asked to figure whether or not the car was speeding before it crashed through the rail of the bridge and into the mudbank. The speed limit on the bridge is 55 mph = 24 m/s. What is your conclusion?( The vertical component is 4.9m/s and the horizontal component is 24 m.)PROJECTILE CONCEPT!!!!!!!!!!
To determine whether or not the car was speeding before it crashed through the rail of the bridge and into the mudbank, we need to analyze the motion of the car using projectile motion concepts.
Given that the speed limit on the bridge is 55 mph = 24 m/s, we can compare this value to the actual speed of the car before the crash. The speed of the car can be determined by finding the magnitude of its velocity vector.
The velocity vector of the car can be broken down into horizontal and vertical components. The horizontal component represents the speed of the car in the direction parallel to the bridge, while the vertical component represents the speed in the vertical direction.
According to the information provided, the horizontal component of the car's velocity is 24 m/s. This means that the car was traveling with a speed of 24 m/s parallel to the bridge.
However, the vertical component of the car's velocity is given as 4.9 m/s. This component represents the car's speed in the vertical direction. Since the vertical component is directed downward (negative), it suggests that the car was descending or falling due to gravity.
In projectile motion, the vertical velocity changes due to the acceleration caused by gravity, while the horizontal velocity remains constant if there are no external forces.
Based on this information, we can conclude that the car was not speeding before the crash. The car's horizontal velocity of 24 m/s is equal to the speed limit. Therefore, it was likely traveling at the maximum permissible speed before the crash.
To determine whether the car was speeding before it crashed, we can analyze the components of its velocity and compare it to the speed limit on the bridge.
Given:
- The speed limit on the bridge is 55 mph = 24 m/s.
- The vertical component of the car's velocity is 4.9 m/s.
- The horizontal component of the car's velocity is 24 m.
We can use the concept of projectile motion to further analyze the situation.
1. Calculate the total velocity of the car:
- Total velocity (V) = square root of (vertical component squared + horizontal component squared)
- V = square root of ((4.9 m/s)^2 + (24 m/s)^2)
- V = square root of (24.01 + 576)
- V = square root of 600.01
- V ≈ 24.49 m/s
2. Compare the car's total velocity with the speed limit:
- Speed limit on the bridge = 24 m/s
- Car's total velocity = 24.49 m/s
Conclusion:
The car's total velocity, 24.49 m/s, exceeds the speed limit of 24 m/s. Therefore, based on the calculations, we can conclude that the car was speeding before it crashed through the rail of the bridge and into the mudbank.